Abstract

The study of Bézier curves, launched by French scientists in the mid 20th century to computer-aided design of car bodies is relevant in the present time. The construction of Bézier curves is performed by using control points, in two of which the curve passes (reference), the other (control) points define the shape of the curve. This allows you to obtain the required curve shape by changing the position of control points. Mathematically the Bezier curves specified by a parametric expression, depending on the coordinates of the control vertices and the Bernstein polynomials. The article considers methods of construction of Bézier curves (based on polynomials of Bernstein, based on the algorithm de Castelle), noted the advantages of each method. The analysis allowed to highlight the most important properties of curves, which are used in various programs of computer-aided design and simulation of smooth lines

Keywords

Bézier curves, reference points, control points, a parametric curve, Bernstein polynomials, algorithm of de Castile, the simulation of smooth lines.